Description taken from Arcade version of this game

You are a ninja. Ninja are silent assassins, trained in the ancient martial arts as well as in modern methods of combat. Some novice female ninja trainees have been kidnapped, and it's up to you to rescue them as well as defeat the evil ninja that kidnapped them.

Each level has a number of kidnapped female ninja who must be rescued. To rescue them you have to touch them, which will free them from their bindings and let them escape. When you've freed all the female ninjas from the level you can proceed to the next level. Every third level is a boss stage. Boss stages have no female ninjas to free. Instead you have to confront a powerful boss character who will require more than one hit to defeat, and has only one vulnerable target.

You have an unlimited supply of throwing stars, as well as a ninja sword, to use in your mission. After freeing some female ninjas you can upgrade to a submachine gun instead of throwing stars. The submachine gun fires in the same way as your stars, but each bullet does more damage. Once during each level you have access to a super attack, which will kill all non-boss enemies on screen. Bosses do not die from super attacks unless they've already been weakened.

Shinobi has a bonus stage between some levels that requires you to throw throwing stars at ninjas from a first person perspective. You stand facing two perpendicular walkways, one further away from you than the other. Enemy ninja will run in on the walkways from the two edges of the screen, and you must kill them with your stars before they stop and jump at you. Enemy ninja from the back walkway will jump to the near walkway, but an enemy ninja who manages to jump from the near walkway will hit you and end the stage. ~ Kyle Knight, All Game Guide